Spin-orbit coupled periodic Anderson model: Kondo-Dirac semimetal and orbital-selective antiferromagnetic semimetal

TL;DR

We study a spin-orbit-coupled periodic Anderson model on a two-dimensional square lattice to understand how SOC in the $c$–$f$ hybridization shapes correlated Dirac semimetal behavior. Using determinant quantum Monte Carlo at half-filling, we map a ground-state phase diagram as a function of the hybridization $V$ and on-site interaction $U$, revealing a Kondo-Dirac semimetal and an orbital-selective antiferromagnetic semimetal, with a quantum transition controlled by $V_c(U)$. The AFM phase exhibits an orbital-selective Mott transition, where the $f$-orbitals open a gap while the $c$-orbitals retain Dirac cones, and the Dirac structure remains robust with moderate Fermi-velocity renormalization; a Gross-Neveu–type universality class governs the quantum critical point with $\nu \approx 1$. The results illuminate the interplay of heavy-fermion physics, SOC, and topology, and suggest routes to topological phases and extensions to three dimensions or doped regimes.

Abstract

We investigate the periodic Anderson model composed of an itinerant $c$-band and a strongly localized $f$-band, featuring on-site electron-electron interactions in the $f$-orbitals. The two bands interact via a hybridization term with spin-orbit coupling, which enables spin-flip processes. In the non-interacting limit, these profoundly alter the electronic structure, leading to the emergence of flat bands, van Hove singularities, and, most notably, Dirac cones within a single Kondo-Dirac semimetal order. The strongly interacting regime is explored via the determinant quantum Monte Carlo method, in the absence of the sign problem, where we unveil a complete ground-state phase diagram revealing two distinct phases, the Kondo-Dirac semimetal phase and a novel antiferromagnetic semimetal phase. Their characterization by the spectral functions establishes an orbital-selective Mott transition in the antiferromagnetic semimetal phase, marked by the opening of a gap exclusively in the $f$-orbital while Dirac cones persist in the $c$-orbital. Conversely, in the Kondo-Dirac semimetal phase, both $c$- and $f$-orbitals sustain robust Dirac cones. We establish that spin-orbit coupling in the hybridization term gives rise to Dirac cones, which, combined with additional symmetry-breaking conditions, can generate novel topological states.

Figures (8)

• Figure 1: (a) Schematic representation of the Periodic Anderson Model (PAM) on a square lattice, where localized $f$-orbitals at each site hybridize with dispersive $c$- electrons through a hybridization $V$ that includes spin–orbit coupling (SOC). Panels (b)–(d) display the tight-binding approximation for the band structure, along a high symmetry path in the Brillouin zone [inset in (b)], and density of states DOS for three regimes: (b) $V=0$, $t=1$; (c) intermediate SOC with $V=0.5$, $t=1$; and (d) pure SOC limit with $V=1$, $t=0$, at zero temperature. Both are resolved by the contributions of the two types of orbitals.
• Figure 2: Magnetic structure factor $S^{\gamma}(\pi,\pi)$ as a function of $\beta t$ for different lattice sizes $L$, under a fixed hybridization $V/t = 0.5$ and on-site electron electron interaction $U/t = 4$. Results for $\gamma = c$- and $f$-orbitals are indicated with dashed and solid lines, respectively. In addition, $\beta$ is the inverse of temperature $T$ ($\beta=1/T$). Inset: Finite-size scaling (FSS) of the magnetic structure factor $S^{\gamma}(\pi,\pi)$ as a function of $1/L$; a finite thermodynamic extrapolation indicates the existence of a finite order parameter.
• Figure 3: (a) [(b)] The correlation ratio $R^{f}$ [$S^{f}(\pi,\pi)$] as a function of the hybridization term $V$, for different lattice sizes $L$. (c) The colormap of the cost function, $C_{R^f}$, in the $\nu-V_c$ plane. The white star locates its minimum, which in turn determines the best fit to the correlation length exponent $\nu$ and $V_{c}$. (d) The cost function for the structure factor $C_{S^f}$ as a function of the anomalous dimension $\eta_\phi$ at the critical point $V_c$. (e) The resulting collapse of $R^{f}$ with fitted $\nu$ and $V_{c}$ from (c), and (f), the resulting collapse of $S^{f}(\pi,\pi)$ with the anomalous dimension $\eta_\phi$. In all panels, we consider the electron-electron interaction $U/t=6$, and a fixed $\beta t=28$, where $\beta$ is the inverse of temperature $T$ ($\beta=1/T$).
• Figure 4: The ground state phase diagram of spin-orbit-coupled (SOC) hybridization $V$ versus on-site electron-electron correlation $U$ in the two-dimensional (2D) periodic Anderson model (PAM). Data points are obtained by compiling the crossing points of the correlation ratio $R^{f}$ vs. $V/t$, as in Fig. \ref{['fig:Collapse']}(a) for different interaction strengths. The dashed line serves as a guide to the eye, inspired by the mean-field results (see Appendix \ref{['App:MFT']}).
• Figure 5: The spectral functions $A^\gamma({\bf k},\omega)$ for both $c$- and $f$-orbitals. In (a), the hybridization with spin-orbit coupling is $V/t=0.6$, in (b) $V/t=0.8$, and in (c) $V/t=1.0$. We consider a fixed on-site electron-electron interaction $U/t=6$ for the $f$-orbitals [the same as in Fig. \ref{['fig:Collapse']}]; linear lattice size is $L=16$, and $\beta t = 28$.